Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form, which is a deformation of the usual basis of Schubert polynomials, and apply it to the computation of the Schubert cycle expansions of Chern classes of flag manifolds.
@article{bwmeta1.element.bwnjournal-article-bcpv36z1p111bwm,
author = {Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
title = {Twisted action of the symmetric group on the cohomology of a flag manifold},
journal = {Banach Center Publications},
volume = {37},
year = {1996},
pages = {111-124},
zbl = {0887.14024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p111bwm}
}
Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves. Twisted action of the symmetric group on the cohomology of a flag manifold. Banach Center Publications, Tome 37 (1996) pp. 111-124. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv36z1p111bwm/
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